Worksheet: Equation of a Straight Line: Vector Form

In this worksheet, we will practice finding the equation of a straight line in vector form.

Q1:

Which of the following can be the vector form of the equation of the straight line π‘Žπ‘₯+𝑏𝑦+𝑐=0, where π‘Žβ‰ 0 and 𝑏≠0?

  • Ar=ο‡²π‘π‘Ž,0ο‡Ά+πΎβŸ¨π‘Ž,βˆ’π‘βŸ©
  • Br=0,βˆ’π‘π‘ο‡Ά+πΎβŸ¨π‘,βˆ’π‘ŽβŸ©
  • Cr=0,𝑐𝑏+πΎβŸ¨π‘,βˆ’π‘ŽβŸ©
  • Dr=ο‡²βˆ’π‘π‘Ž,0ο‡Ά+πΎβŸ¨π‘Ž,βˆ’π‘βŸ©
  • Er=ο‡²π‘π‘Ž,0ο‡Ά+πΎβŸ¨π‘Ž,π‘βŸ©

Q2:

Which of the following can be the vector form of the equation of the straight line π‘₯π‘Ž+𝑦𝑏=1, where π‘Žβ‰ 0 and 𝑏≠0?

  • Ar=βŸ¨π‘Ž,0⟩+πΎβŸ¨π‘Ž,βˆ’π‘βŸ©
  • Br=ο€Ό0,1π‘Žοˆ+𝐾(βˆ’π‘,π‘Ž)
  • Cr=⟨0,π‘βŸ©+πΎβŸ¨π‘Ž,π‘βŸ©
  • Dr=0,1𝑏+πΎβŸ¨π‘,π‘ŽβŸ©
  • Er=ο‡³βˆ’1π‘Ž,0ο‡·+πΎβŸ¨π‘,βˆ’π‘ŽβŸ©

Q3:

Find the vector equation of the straight line passing through the origin and the point (0,4).

  • Ar=⟨0,4⟩
  • BrK=⟨4,0⟩
  • Cr=⟨4,0⟩
  • DrK=⟨0,4⟩

Q4:

Find the vector equation of the straight line passing through the points (6,βˆ’7) and (βˆ’4,6).

  • Ar=βŸ¨βˆ’4,6⟩+πΎβŸ¨βˆ’13,10⟩
  • Br=βŸ¨βˆ’4,6⟩+𝐾⟨10,13⟩
  • Cr=⟨6,βˆ’7⟩+𝐾⟨10,βˆ’13⟩
  • Dr=⟨6,βˆ’4⟩+πΎβŸ¨βˆ’7,6⟩

Q5:

Find the vector equation of the straight line whose slope is βˆ’83 and passes through the point (4,βˆ’9).

  • Ar=⟨3,βˆ’8⟩+𝐾⟨4,βˆ’9⟩
  • Br=⟨4,βˆ’9⟩+𝐾⟨8,βˆ’3⟩
  • Cr=βŸ¨βˆ’9,4⟩+𝐾⟨3,βˆ’8⟩
  • Dr=⟨4,βˆ’9⟩+𝐾⟨3,βˆ’8⟩

Q6:

Consider the line through the point (3,6) and perpendicular to vector r=⟨3,6⟩. Which of the following is a vector equation of this line?

  • A𝐾=⟨3,6⟩+⟨6,βˆ’3⟩r
  • Br=⟨3,6⟩+𝐾⟨6,βˆ’3⟩
  • Cr=⟨3,6⟩+𝐾⟨3,6⟩
  • Dr=⟨6,βˆ’3⟩+𝐾⟨3,6⟩
  • E𝐾=⟨3,6⟩+⟨3,6⟩r

Q7:

Write the vector equation of the straight line that passes through the point βŸ¨βˆ’6,βˆ’9⟩ with direction vector ⟨9,βˆ’2⟩.

  • ArK=⟨9,βˆ’2⟩+βŸ¨βˆ’6,βˆ’9⟩
  • BrK=βŸ¨βˆ’6,βˆ’9⟩+⟨9,βˆ’2⟩
  • CKr=⟨9,βˆ’2⟩+βŸ¨βˆ’6,βˆ’9⟩
  • DKr=βŸ¨βˆ’6,βˆ’9⟩+⟨9,βˆ’2⟩

Q8:

Find the vector equation of the straight line that is parallel to the π‘₯-axis and passing through the point (βˆ’5,2).

  • ArK=⟨2,βˆ’5⟩+⟨1,0⟩
  • BrK=βŸ¨βˆ’5,2⟩+⟨1,0⟩
  • CrK=⟨2,βˆ’5⟩+⟨0,1⟩
  • DrK=βŸ¨βˆ’5,2⟩+⟨0,1⟩

Q9:

Consider the line through the point (0,4) and perpendicular to vector r=⟨0,4⟩. Which of the following is a vector equation of this line?

  • A𝐾=⟨0,4⟩+⟨4,0⟩r
  • Br=⟨0,4⟩+𝐾⟨4,0⟩
  • Cr=⟨0,4⟩+𝐾⟨0,4⟩
  • Dr=⟨4,0⟩+𝐾⟨0,4⟩
  • E𝐾=⟨0,4⟩+⟨0,4⟩r

Q10:

Given that (9,1) and (βˆ’8,π‘š) are the direction vectors of two perpendicular straight lines, determine the value of π‘š.

  • A72
  • Bβˆ’72
  • Cβˆ’89
  • D89

Q11:

Suppose that a line has direction vector u=⟨21,4⟩. What, to the nearest second, is the measure of the positive angle that this line makes with the positive π‘₯-axis?

  • A16912β€²57β€²β€²βˆ˜
  • B7912β€²57β€²β€²βˆ˜
  • C10047β€²3β€²β€²βˆ˜
  • D1047β€²3β€²β€²βˆ˜

Q12:

If the straight line that passes through the two points (π‘˜,6) and (βˆ’2,βˆ’2) is perpendicular to the one that makes an angle of 14759β€²40β€²β€²βˆ˜ with the positive direction of the π‘₯-axis, find the value of π‘˜ to the nearest integer.

  • Aβˆ’8
  • Bβˆ’7
  • C3
  • Dβˆ’13

Q13:

Which of the following is a direction vector of the straight line π‘Žπ‘₯+𝑏𝑦+𝑐=0?

  • A(π‘Ž,𝑏)
  • B(𝑏,βˆ’π‘Ž)
  • C(βˆ’π‘Ž,βˆ’π‘)
  • D(π‘Ž,βˆ’π‘)
  • E(𝑏,π‘Ž)

Q14:

Which of the following is a directional vector for a line perpendicular to the π‘₯-axis?

  • Aj=⟨0,1⟩
  • Bi=⟨1,0⟩

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